   Chapter 11.4, Problem 45E

Chapter
Section
Textbook Problem

# Magnitude When the magnitudes of two vectors are doubled, how will the magnitude of the cross product of the vectors changes? Explain.

To determine

How the magnitude of the cross product of two vectors will change if their magnitude is doubled.

Explanation

Let vector u and v are u=u1i+u2j+u3k and v=v1i+v2j+v3k.

Evaluate the cross product u×v. The cross product of two vector a=a1i+a2j+a3j and b=b1i+b2j+b3k is:

a×b=|ijka1a2a3b1b2b3|

Therefore, the cross product u×v for vectors u=u1i+u2j+u3k and v=v1i+v2j+v3k is,

u×v=|ijku1u2u3v1v2v3|

On simplification,

u×v=(u2v3u3v2)i(u1v3u3v1)j+(u1v2u2v1)k

The magnitude of the vector u×v is,

u×v=(u2v3u3v2)2+(u1v3u3v1)2+(u1v2u2v1)2

Now, if the magnitude of the vectors u and v is doubled then the vectors become 2u and 2v and each component of the vectors get multiplied by 2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the limit, if it exists. limx164x16xx2

Single Variable Calculus: Early Transcendentals

#### x234x5

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 15-26,evaluate each expression. 15.

Mathematical Applications for the Management, Life, and Social Sciences 